Total variation based tensor decomposition for multi-dimensional data with time dimension

Chuan Chen, Xutao Li, Kwok Po NG*, Xiaoming YUAN

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we study tensors with time dimension which arises in many scientific and engineering applications such as time series gene expression analysis and video analysis. In these applications, we are interested in determining a set of components interacting closely and consistently together over a period of time. The main aim of this paper is to develop a numerical method to compute such constrained CANDECOMP/PARAFAC (CP) decompositions. We make use of the total variation regularization to constrain the time dimension factor in the decomposition in order to obtain a piecewise constant function with respect to time points. The components of the other dimensions corresponding to these time points are closely related. For example, in time series gene expression analysis, a set of genes may regulate a biological process together during a specific time period; in video analysis, a set of image pixels may refer to a foreground object in the video frames. We employ ADMM to solve the resulting optimization problem, and study its convergence. Numerical examples on synthetic and real data sets are used to demonstrate that the proposed total variation based CP decomposition model can provide more accurate and interesting results.

Original languageEnglish
Pages (from-to)999-1019
Number of pages21
JournalNumerical Linear Algebra with Applications
Volume22
Issue number6
DOIs
Publication statusPublished - 1 Dec 2015

Scopus Subject Areas

  • Algebra and Number Theory
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method of multipliers
  • Multidimensional data
  • Regularization
  • Tensor decomposition
  • Time dimension
  • Total variation

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